Consider the dynamics given below.

$x_1=f_1(x,u)=x_2$

$x_2=f_2(x,u)=-0\mathrm{.}4x_1+0\mathrm{.}2x_3-0\mathrm{.}1x_2{x}_3$

$x_3=f_3(x,u)=-0\mathrm{.}75x_3-0\mathrm{.}025x_3^3+1\mathrm{.}5x_1+2u$

Lincarize the system about an equilibrum resulting from $u_{eq}=0\mathrm{.}15.(20$ points$)$

Hint: You noed to first find the equilibrium for $x.$ You can then use $x^{}=Ax+Bu$ where $A=$